Multi-robot Path Planning and Trajectory Smoothing

In this paper we consider a problem in task execution for multi-robot trajectory planning with collision avoidance in a shared working environment. Consider two or more robots generating trajectories towards their respective goal positions. The collision may occur if their trajectory coordinates are intersecting at a point or follow the same path segment simultaneously. The central planner is introduced to control robot motion in the collision state and to reduce the complexity of the multi-robot path planning system. The global path for every robot is generated by the $\mathrm{A}^{*}$ algorithm in a grid-based environment. The path has presented a sequence of optimal grid numbers and later transformed into Cartesian coordinates for smooth trajectory generation. The central planner takes an optimal grid sequence for every robot to analyze the collision state according to its cost value. It regenerates the trajectories to minimize the complexity cost value and replaces the previous trajectory based on minimum cost value. In the collision state, the central planner allows one robot at a time to pass along the conflict path segment and hold others in queue at a safety offset distance until the previous robot passes safely. The algorithm has been applied to robots working in a shared environment in complex maps and the simulations is performed with MATLAB to calculate the efficiency of this approach for handling collision states in a multi-robot path planning system.